(A) Given expression: $p(p^{2}+3p+3)$$= p^{3}+3p^{2}+3p$To complete the algebraic identity $(p+1)^{3} = p^{3}+3p^{2}+3p+1$,we add and subtract $1$:$=

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(A) Given expression: $p(p^{2}+3p+3)$$= p^{3}+3p^{2}+3p$To complete the algebraic identity $(p+1)^{3} = p^{3}+3p^{2}+3p+1$,we add and subtract $1$:$= (p^{3}+3p^{2}+3p+1) - 1$$= (p+1)^{3} - 1$Substitute $p=99$:$= (99+1)^{3} - 1$$= 100^{3} - 1$$= 1000000 - 1$$= 999999$